Question

	Year-Year Percent Change in Commodities CPI	Year-Year Percent Change in Services CPI
Year	Commodities%	Services%
1960	0.9	3.4
1961	0.6	1.7
1962	0.9	2.0
1963	0.9	2.0
1964	1.2	2.0
1965	1.1	2.3
1966	2.6	3.8
1967	1.9	4.3
1968	3.5	5.2
1969	4.7	6.9
1970	4.5	8.0
1971	3.6	5.7
1972	3.0	3.8
1973	7.4	4.4
1974	11.9	9.2
1975	8.8	9.6
1976	4.3	8.3
1977	5.8	7.7
1978	7.2	8.6
1979	11.3	11.0
1980	12.3	15.4
1981	8.4	13.1
1982	4.1	9.0
1983	2.9	3.5
1984	3.4	5.2
1985	2.1	5.1
1986	-0.9	5.0
1987	3.2	4.2
1988	3.5	4.6
1989	4.7	4.9
1990	5.2	5.5
1991	3.1	5.1
1992	2.0	3.9
1993	1.9	3.9
1994	1.7	3.3
1995	1.9	3.4
1996	2.6	3.2
1997	1.4	3.0
1998	0.1	2.7
1999	1.8	2.5
2000	3.3	3.4
2001	1.0	4.1
2002	-0.7	3.1
2003	1.0	3.2
2004	2.3	2.9
2005	3.6	3.3
2006	2.4	3.8

1)Attach the output. Construct a scatter plot. Recalling what scatter plots are used for, write a couple of sentences addressing what you observed from the plot. Be sure to relate your observations to the purpose of using scatter plots in regression. (4 points)

2)Can we conclude that year-to-year changes in Commodities percentage (Commodities%) helps in predicting year-to year changes in Services percentage (Services%)? Follow and show the 7 steps for hypothesis testing. (12 points)

3)Find the sample regression equation and interpret the coefficients. Remember your interpretations should be in terms of the problem. (4 points)

4)Find the coefficient of determination, and interpret its value. (3 points)

5)Use residual analysis to check the validity of the model and fully explain your findings and conclusions. (6 points)

6)Estimate with 95% confidence the average year-to-year Services percentage for when all year-to-year Commodities change is 3.0%. Predict with 95% confidence the estimated Services percentage when an individual year’s Commodities change is 3.0%. Write at least one sentence using your confidence interval and at least one sentence using your prediction interval. (8 points)

7)Verify that the p-value for the F is the same as the slope’s t statistic’s p-value, and show that t2 = F. (3 points)

Answer 1